⟨a, b | aabbaabbba=1⟩

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Monoids with two generators and one relation

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Auxiliary generators:
1. c = aaa
2. d = bbaabbb
Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[9]
2.	dc ⇒ 1	[11]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[10]
5.	a³ ⇒ c	[2]
6.	cb²a²b ⇒ bcb²a²	[23]
7.	dbcb² ⇒ b²a²bda	[17]
8.	ab²a²b ⇒ b³c	[15]
9.	abcb² ⇒ cb³a	[20]
10.	a²b³ ⇒ bcb²da²	[26]
11.	db²cb² ⇒ b²a²b²da	[18]
12.	ab²cb² ⇒ cb³cbda	[22]
13.	b³cb² ⇒ da	[16]
14.	cb²ab³ ⇒ (b²c)²abd	[28]
15.	cb²cab³ ⇒ bcb²ca²b²da²	[31]
16.	ab²ab³ ⇒ b³cba²bd	[27]
17.	ab²cab³ ⇒ b³c²b²da²	[30]

# ab:aabbaabbba=1 cda/b aaa=c,bbaabbb=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c cbbaab=bcbbaa dbcbb=bbaabda abbaab=bbbc abcbb=cbbba aabbb=bcbbdaa dbbcbb=bbaabbda abbcbb=cbbbcbda bbbcbb=da cbbabbb=bbcbbcabd cbbcabbb=bcbbcaabbdaa abbabbb=bbbcbaabd abbcabbb=bbbccbbdaa

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

Σ	#	Presentation	Mapping
10	1459	⟨a, b \| aabbbaaabb=1⟩	φ(a) = a, φ(b) = b
10	1461	⟨a, b \| aabbbaabba=1⟩	φ(a) = b, φ(b) = a
10	1530	⟨a, b \| abbaaabbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

1459

⟨a, b | aabbbaaabb=1⟩

φ(a) = a, φ(b) = b

1461

⟨a, b | aabbbaabba=1⟩

φ(a) = b, φ(b) = a

1530

⟨a, b | abbaaabbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#1445 ⟨a, b \| aabbaabbab=1⟩
Next:	#1449 ⟨a, b \| aabbabaabb=1⟩

#1446 ⟨a, b | aabbaabbba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances